Question

To find the velocity and acceleration vectors for uniform circular
motion and to recognize that this acceleration is the centripetal
acceleration.
Suppose that a particle's position is given by the following
expression:

a) When does the particle first cross the negative x axis?
b)Find the particle's velocity as a function of time.
c)Find the speed of the particle at time t.
d)Now find the acceleration of the particle.
e)Your calculation is actually a derivation of the centripetal
acceleration. To see this, express the acceleration of the particle
in terms of its position r_vec(t).